For various known reasons, electrical motors and generators cannot operate perfectly, and several factors can detract from the overall efficiency. For example, cogging torque is caused by the magnetic attraction between the magnets of the rotor and the stator slots or stator teeth. In a homogenous arrangement in which the magnets/stator slots are all placed equidistantly, for a certain position of the rotor relative to the stator, the magnetic attraction between the magnets and the stator slots is relatively large. Small motors and generators can usually be satisfactorily optimised. However, in a large machine such as a 3 MW generator in a wind turbine, the cogging torque can easily reach values of 5% of nominal torque. Since this force must be overcome at start-up and many times during each rotation of the rotor, it can have a large impact on the performance of the generator, shortening its lifespan and increasing its noise level. Therefore, measures are usually taken during generator design to reduce the cogging torque.
Another problem is presented by torque ripple, which is the sum of cogging torque and the additional torque variations caused by harmonics in the air gap flux of the machine. Sources of these harmonics are usually the iron of the stator, the distances between rotor magnets and stator, etc. Choosing the number of stator slots to be a multiple of the number of magnets can help reduce the torque ripple by some amount. However, torque ripple can still have a detrimental impact on the efficiency, life time and noise level of the generator.
There are various ways of optimising the performance of an electrical generator. However, the known approaches are quite complicated. For example, to minimise cogging torque, which is caused when the magnets or poles are simultaneously dragged towards the stator teeth, re-arranging the poles in a process known as ‘pole shifting’ so that they are no longer placed equidistantly to each other can result in a lessening of the cogging torque. However, the improvement will only be ideal for a given rotor position for each stator tooth. Also, the torque ripple may even increase when the poles are shifted with the aim of reducing cogging. However, simulation of a pattern of shifted poles is very cost-intensive, since, according to a rule of thumb, the computation time increases exponentially with increasing poles, so that patterns containing many poles result in very long computation times.
Since the various performance parameters such as cogging and ripple do not have the same optimum, it is necessary to settle for a compromise or trade-off. For example, if cogging is minimised, it is not possible to minimise ripple at the same time. Another important consideration is that pole shifting will always result in a reduction in back emf (electromotive force) and running torque, which is usually a drawback, and the extent of the influence depends on the chosen pole shifting pattern.
Known approaches use software algorithms to simulate the performance of a generator in the light of known parameters such as magnet placement, certain load conditions, etc. However, the iron generally used for the stator and other parts is quite saturated, making the equations very nonlinear and complex. Accurate analysis requires numerical field solutions. The more variables are altered in striving for an optimal solution, the more complicated the analysis becomes. Factors such as manufacturing tolerances such as eccentricity can result in real-life performance that does not fulfil the (simulated) expectations, since the modelled geometry is considerably different from the actual manufactured machine. In approaches based on pole-shifting many magnets with respect to each other, a minor ‘error’ in the machine geometry can easily negate the benefits of the pole-shifting.